During a flight of the aircraft, such a navigation system serves to calculate successive positions of the aircraft by making use of a main filter for merging data coming from a constellation of visible satellites that are present above a horizon of the aircraft, and possibly also data coming from an inertial navigation unit or the like on board the aircraft. It is recalled that the horizon is the line separating that which is masked from the aircraft by the curvature of the earth from that which is not masked thereby. With the GPS system, some maximum number of satellites can be present above the horizon of an aircraft (i.e. there will be some maximum number of satellites that are not masked from the aircraft by the curvature of the earth), and this number is about ten. However, it is not unusual for geographical relief or a portion of the aircraft to mask one or more of the satellites. Nevertheless, the navigation system remains operational providing it has data available from at least four satellites making up the constellation of visible satellites. The navigation system is found to be particularly accurate when the satellites are operating correctly, however its performance falls off quickly as soon as one of the satellites presents a failure that affects the validity of the data it transmits.
To remedy that problem, the navigation system also calculates corrected positions from additional filters, each of which excludes data coming from one of the satellites. When failure of one of the satellites is detected, the additional filter that excludes that particular satellite becomes the main filter, and the other additional filters are initialized from the new main filter.
The creation of additional filters is triggered by detecting a new satellite. Thus, as soon as the data coming from a satellite reaches the navigation system, an additional filter excluding that satellite is created and the satellite is incorporated in the existing additional filters. When the navigation system no longer detects data coming from that satellite, the corresponding additional filter is deleted. Unfortunately, when satellites are masked by geographical relief or by a portion of the aircraft, the data transmitted by the masked satellites no longer reach the navigation system, thereby causing the corresponding filters to be deleted, which filters will be recreated when the satellites are no longer masked and data from them again reaches the navigation system. Managing additional filters is particularly burdensome and constitutes a major computation load for the navigation system.